Cylinder Renormalization of Siegel

Siegel Disks and Renormalization Fixed Points

In this note we construct hyperbolic fixed points for cylinder renormalization of maps with Siegel disks.

Cylinder renormalization for Siegel disks and a constructive Measurable Riemann Mapping Theorem

The boundary of the Siegel disk of a quadratic polynomial with an irrationally indifferent fixed point with the golden mean rotation number has been observed to be self-similar. The geometry of this self-similarity is universal for a large class of holomorphic maps. A renormalization explanation of this universality has been proposed in the literature. However, one of the ingredients of this ex...

A ug 2 00 6 CYLINDER RENORMALIZATION OF SIEGEL DISKS

We study one of the central open questions in one-dimensional renormalization theory – the conjectural universality of golden-mean Siegel disks. We present an approach to the problem based on cylinder renormalization proposed by the second author. Numerical implementation of this approach relies on the Constructive Measurable Riemann Mapping Theorem proved by the first author. Our numerical stu...

Cylinder Renormalization of Siegel Disks

We study one of the central open questions in one-dimensional renormalization theory – the conjectural universality of golden-mean Siegel disks. We present an approach to the problem based on cylinder renormalization proposed by the second author. Numerical implementation of this approach relies on the Constructive Measurable Riemann Mapping Theorem proved by the first author. Our numerical stu...

A Methodology Based on Experimental Investigation of a DBD-Plasma Actuated Cylinder Wake for Flow Control